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Measure and Topology

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Real and Functional Analysis
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Abstract

As the chapter title indicates, our purpose here is to study measures on classes of subsets of certain topological spaces. Given a topological space X, measures with pertinent properties will be studied on σ-rings and σ-algebras generated by the compact subsets of X, the closed subsets of X, the compact G δ subsets of X, or others. For the most part, X will be taken as a locally compact topological space.

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References

  • F. Riesz, Sur les opérations fonctionnelles linéaires, C. R. Acad. Sci. Paris 149, 974–977 (1909).

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  • E. Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37, 161–189 (1950).

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  • R. Edwards, A theory of Radon measures on locally compact spaces, Acta Math. 89, 133–164 (1953).

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© 1978 Springer Science+Business Media New York

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Mukherjea, A., Pothoven, K. (1978). Measure and Topology. In: Real and Functional Analysis. Mathematical Concepts and Methods in Science and Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2331-0_7

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  • DOI: https://doi.org/10.1007/978-1-4684-2331-0_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-2333-4

  • Online ISBN: 978-1-4684-2331-0

  • eBook Packages: Springer Book Archive

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